As an example, we illustrate it in the cases \(\mathcal {V}_{m,0}\)  and \(\mathcal {V}_{0,n}\) , that have been previous handled using a different argument
in [1]} and [2]}. In the case \(\mathcal {V}_{m,0}\)  we have \(\mathrm {ht}(\lambda ) \le m\) , therefore the space of invariants
is generated by Chern classes \(c_i\)  of degree \(2i\) , for \(1 \le i \le m\)  (corresponding to columns of height \(i\) ), with the condition
that the total degree is less or equal than \(2m\)  (the height of the first column).
